I'll try to respond to your post, Moonshine Fox, in a very long and thorough way. Just a little background information, my chosen field of study is Psychology, so I'm devoting my entire career to helping people with the kinds of problems and "dilemmas" you're experiencing right now. I would say that I'm already very good at it, as I have helped, or am in the process of helping, many of my friends through serious relationship issues, with solutions that they would have never expected to have been given.
The first thing you have to realize, before you can have any measure of success in a relationship in our society (in my opinion), is that our entire way of viewing love and relationships is completely wrong. People think they know what love is, and they think they know what it means to be in a healthy relationship, but what you actually find when you look at the statistics is that most relationships in our culture fail miserably. The lessons that we are taught about love and commitment are, in actuality, extremely off the mark, and so if you want to understand what makes for a good romantic relationship, or even a good friendship with the opposite sex, you kind of need to throw out everything you think you "know", and start over.
To answer the original question of the OP: Yes, a male/female friendship relationship is possible. However, the "without love interfering" is a non-sequitur. You can't have a friendship without love; at least not a very deep one. I wouldn't call any of my "friends" who I don't love friends, I would call them acquaintances, or the equivalent to Facebook friends. They're fun to talk to and hang out with sometimes, but I don't have a deep connection with them (certainly not the one you're describing with this girl), and I wouldn't particularly be that upset if they disappeared from my life.
Going back to what I said just a couple paragraphs earlier, society will tell you that a healthy non-romantic relationship between a male and a female is impossible. This is absolutely absurd, and I don't think any rational person could, or should believe it.
A bit of personal evidence:
1. I have a very close relationship with a previous girlfriend. We were actually extremely close when we were together, we had sex and planned to spend our entire lives together. It didn't work out for various reasons. She actually stopped talking to me for several years after it ended, angry and bitter about the relationship; but I never stopped loving her, and I never stopped expressing my love to her. Two years later, she came back, and now we are the best of friends. We talk to each other all the time, and we are like a light in the darkness of each other's lives. We realize that though we both did some hurtful things to each other when we were together, it was never our intention to hurt the other person, we were both just learning and discovering life together. All hard feelings between us are gone, and now there is only love, peace and friendship.
So how did this happen? It happened for the exact reason I said it did: I never stopped loving her. I never gave up on her. I didn't really care whether she returned my love or not.
2. I have another close relationship with a previous girlfriend. She is married and has a child with another man. But we are still close. We tell each other "I love you" all the time. We talk about our past. She talks about her life, and how much she loves her kid. Sometimes she laments that we couldn't have been together instead (her husband is kind of an abusive ass).
Our society would tell you that you can't "love" a married woman, and that a married woman can't "love you".
So how is this possible? Love isn't based on conditions. See the first example. I love Kayla whether she's married or not. What does that have to do with it?
3. I have countless other girls in a state of distance from me. Yet, their inability or choice not to physically return my love does not hamper my ability to love them. In fact, in some ways, it makes me love them more because I know they need love. Just like my first 2 examples, they will one day return to me and we will have good relationships as well, even if we are not "together" romantically.
So yes, it's possible to have a relationship with a female, or male, or anybody, without being "romantically" involved in the classical sense. It's not possible to be in a relationship with a male, or female, or anybody (in my opinion), without loving them.
If you want to know how this is possible, then you have to understand the meaning of love. Our society defines love roughly as an agreement between two people. Person A) chooses to love Person B), and Person B) chooses to love Person A). It gets even weirder after that. Now that two people have made a rough "agreement" to love each other (lol), they begin to quantify the value of their "love".
If Person A) is a man, and he works 60 hours a week, then that means he must love Person B), a woman, a lot. Person B) is expected to, in return, meet that value with sexual favors, and/or by doing the housework, washing his clothes, making dinner, etc.
The point here is that love in our society is quantified. The stereotypical gender roles don't matter. Person A) could be the woman and Person B) could be the man. The "methods of showing love" and values arbitrarily defined to them could be anything.
The entire point is that A. Love is a mutual agreement between two people and B. Each person is expected to give roughly the same amount of "love" through perceived quantifications of physical actions.
In actuality, this "philosophy", if you want to call it that, has absolutely nothing to do with love. And if you want to understand what love really is, and what a healthy relationship is, then the first thing you have to do, is throw it out.
If you'd like to know more, I can keep going.
